Find the remainder when $3x^3-4x^2+2x-5$ is divided by $x-2$.

Step 1 ：Step 1: Write the dividend and the divisor in long division format. We are looking for the quotient and the remainder when dividing $3x^3-4x^2+2x-5$ by $x-2$.

Step 2 ：Step 2: Divide the first term of the dividend by the first term of the divisor, that is, $\frac{3x^3}{x}=3x^2$. Write this term above the division bar.

Step 3 ：Step 3: Multiply the divisor $x-2$ by the term $3x^2$ obtained in Step 2 and subtract this from the original dividend to obtain a new dividend.

Step 4 ：Step 4: Repeat the process with the new dividend. Divide $-2x^2$ by $x$ to get $-2x$, write it above the division bar, and subtract $-2x\ast (x-2)$ from the new dividend.

Step 5 ：Step 5: Repeat the process with the new dividend. Divide $6x$ by $x$ to get $6$, write it above the division bar, and subtract $6\ast (x-2)$ from the new dividend.

Step 6 ：Step 6: Now we cannot proceed further as the degree of the remaining dividend $7$ is less than the degree of the divisor $x-2$. So, $7$ is the remainder when $3x^3-4x^2+2x-5$ is divided by $x-2$.